900 year New England temp record meets Shannon's sampling theorem

A post in Phys.org claims to have used a new method to find and plot the temperature recorded in the bottom of a deep Maine lake.  They perform some unspecified analysis of a chemical that I have never heard of to determine the temperature of long ago.  They don't explain this bit of chemistry at all.  They claim to have taken 136 measurements over some 900 years of lake bottom sediments.  And they claim to have discovered previously unknown temperature variations of 50-60 year duration.
Good paper,  the authors feel they have made a breakthru.
I think they have not taken enough samples.  Temperature in Maine can get up to 90F in the summer, I've been there, I know, and Maine winter runs 20F with cold snaps down as far as -40F.  And  this temperature variation, 70 to 130 degrees, happens quite regularly, summer and winter happen every year.  So we only take 136 samples over 900 summers and winters.  Suppose our samples hit mostly summer for a few years?  Bingo, a heat wave wave, global warming strikes early.  Suppose our samples only hit winter for a few more years in a row?  Bingo, a mini ice age.  
   To do this right, you have to take at least two samples for every year.  That's Shannon's Sampling Theorem, you have to sample twice in the period of the highest frequency  in the signal you are sampling.  If you don't take enough samples, you get aliasing.  That is what causes the wheels of the stagecoach to start turning backwards as the stage gathers speed on the way out of Deadwood.  The movie camera samples the wheels 24 frames per second.  When the wheel spokes move too much in between camera frames, the wheel appears to move in reverse. 
   This paper claims to find 10  different 50-60 year periods of heat or cold.  Since they are not taking enough samples, they could well be seeing an alias.  Their samples  just happen to hit summer for a long stretch of years, or just happen to hit winter for a long stretch of years.  That's aliasing, and will show you imaginary hot spells and cold spells.  Just as imaginary as the stagecoach wheels running backwards.
  About the best you can do with this under sampled data is divvy it up into convenient slices, say 100 years each, and take the average over each 100 year slice.  Then you can look for temperature changes from century to century.